1. Topology and Dynamics of Complex Networks
FRES1010
Complex Adaptive Systems
Eileen Kraemer
Fall 2005

2. Based on … Strogatz (2001), Barabási & Bonabeau (2003),
Wang, X. F. (2002)

3. Topology and Dynamics of Complex Networks
Introduction
Three structural metrics
Four structural models
Structural case studies
Node dynamics and self-organization
Bibliography

4. Introduction Examples of complex networks Elementary features
Motivations

5. Examples of complex networks: geometric, regular

6. Examples of complex networks: semi-geometric, irregular

7. Elementary features: node diversity and dynamics

8. Elementary features: edge diversity and dynamics

9. Elementary features: Network Evolution

10. Motivations complex networks are the backbone of complex systems
every complex system is a network of interaction among numerous smaller elements
some networks are geometric or regular in 2-D or 3-D space
other contain “long-range” connections or are not spatial at all
understanding a complex system = break down into parts + reassemble
network anatomy is important to characterize because structure affects function (and vice-versa)
ex: structure of social networks
prevent spread of diseases
control spread of information (marketing, fads, rumors, etc.)
ex: structure of power grid / Internet
understand robustness and stability of power / data transmission

11. Three structural metrics
Average path length
Degree distribution(connectivity)
Clustering coefficient

12. Structural metrics: Average path length

13. Structural Metrics: Degree distribution(connectivity)

14. Structural Metrics: Clustering coefficient

15. Four structural models
Regular networks
Random networks
Small-world networks
Scale-free networks

16. Regular networks – fully connected

17. Regular networks – Lattice

18. Regular networks – Lattice: ring world

19. Random networks

20. Random Networks

21. Small-world networks

22. Small-world networks

23. Small-world networks

24. Small-world networks

25. Scale-free networks

26. Scale-free networks

27. Scale-free networks

28. Scale-free networks

29. Scale-free networks

30. Scale-free networks

31. Case studies Internet World Wide Web Actors & scientists
Neural networks
Cellular metabolism

32. The Internet

33. The Internet

34. The Internet

35. The World Wide Web

36. World Wide Web

37. World Wide Web

38. Actors

39. Mathematicians & Computer Scientists

40. Node dynamics and self-organization
Attractors in full & lattice networks
Synchronization in full networks
Waves in lattice networks
Epidemics in complex networks

41. Node dynamics: individual node

42. Node dynamics: coupled nodes

43. Node dynamics and self-organization

44. Node dynamics and self-organization

45. Node dynamics and self-organization

46. Node dynamics and self-organization

47. Node dynamics and self-organization

48. Node dynamics and self-organization: Epidemics in complex networks

49. Node dynamics and self-organization: Epidemics in complex networks

50. Bibliography
Reviews
Barabási, A.-L. (2002) Linked: The New Science of Networks.Perseus Books.
Barabási, A.-L. and Bonabeau, E. (2003) Scale-free networks. Scientific American, 288:
Strogatz, S. H. (2001) Exploring complex networks. Nature, 410(6825):
Wang, X. F. (2002) Complex networks: topology, dynamics and synchronization. International Journal of Bifurcation and Chaos, 12(5):

51. Bibliography
Studies
Albert, R., Jeong, H. & Barabási, A.-L. (1999) Diameter of the World Wide Web. Nature401:
Albert, R., Jeong, H. & Barabási, A.-L. (2000) Attack and error tolerance in complex networks. Nature406:
Barabási, A.-L. and Albert, R. (1999) Emergence of scaling in random networks. Science, 286(5439):
Erdős, P. & Rényi, A. (1960) On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci.5:
Faloutsos, M., Faloutsos, P. & Faloutsos, C. (1999) On power-law relationships of the Internet topology. Comput. Commun. Rev.29:
Pastor-Satorras, R. & Vespignani, A. (2001) Epidemic dynamics and endemic states in complex networks. Phys. Rev.E63(066117): 1-8.
Watts, D. J. and Strogatz, S. H. (1998) Collective dynamics of "small-world" networks. Nature, 393(6684):